The HCF and LCM of the two numbers are 21 and 84 respectively. If the ratio of the two numbers is 1 : 4 then the larger of the two numbers is =?

Question: The HCF and LCM of the two numbers are 21 and 84 respectively. If the ratio of the two numbers is 1 : 4 then the larger of the two numbers is =?

Solution:
We know,
LCM × HCF = 1^st number × 2^nd number

Let 1^st number = P
2^nd number = 4P

P × 4P = 21 × 84
⇒ 4P² = 21 × 84
⇒ P² = 21 × 21
∴ P = 21

Then, the numbers = 21, 84
So, the larger number = 84